Problem: Recently Duff has been a soldier in the army. Malek is her commander.

Their country, Andarz Gu has n cities (numbered from 1 to n) and n - 1 bidirectional roads. Each road connects two different cities. There exist a unique path between any two cities.

There are also m people living in Andarz Gu (numbered from 1 to m). Each person has and ID number. ID number of i - th person is i and he/she lives in city number ci. Note that there may be more than one person in a city, also there may be no people living in the city.

<image>

Malek loves to order. That's why he asks Duff to answer to q queries. In each query, he gives her numbers v, u and a.

To answer a query:

Assume there are x people living in the cities lying on the path from city v to city u. Assume these people's IDs are p1, p2, ..., px in increasing order. 

If k = min(x, a), then Duff should tell Malek numbers k, p1, p2, ..., pk in this order. In the other words, Malek wants to know a minimums on that path (or less, if there are less than a people).

Duff is very busy at the moment, so she asked you to help her and answer the queries.

Input

The first line of input contains three integers, n, m and q (1 ≤ n, m, q ≤ 105).

The next n - 1 lines contain the roads. Each line contains two integers v and u, endpoints of a road (1 ≤ v, u ≤ n, v ≠ u).

Next line contains m integers c1, c2, ..., cm separated by spaces (1 ≤ ci ≤ n for each 1 ≤ i ≤ m).

Next q lines contain the queries. Each of them contains three integers, v, u and a (1 ≤ v, u ≤ n and 1 ≤ a ≤ 10).

Output

For each query, print numbers k, p1, p2, ..., pk separated by spaces in one line.

Examples

Input

5 4 5
1 3
1 2
1 4
4 5
2 1 4 3
4 5 6
1 5 2
5 5 10
2 3 3
5 3 1


Output

1 3
2 2 3
0
3 1 2 4
1 2

Note

Graph of Andarz Gu in the sample case is as follows (ID of people in each city are written next to them):

<image>

Solution (in JAVA):

Solution:
import java.util.*;
import java.util.Map.Entry;
import java.io.*;
import java.lang.*;
import java.math.*;

import static java.lang.Math.*;

public class Solution implements Runnable {
	
	final int K = 10;
	
	ArrayList<Integer>[] g;
	int[][][] id;
	int[][] pr;
	int[][] k;
	int ln;
	int[] a, b, c;
	
	int union(int[] a, int[] b, int[] c, int na, int nb) {
		int nc = 0;
		for (int i = 0, j = 0; (i < na || j < nb) && nc < K; ) {
			if (i < na && j < nb) {
				if (a[i] < b[j]) {
					if (nc == 0 || c[nc - 1] != a[i])
						c[nc++] = a[i];
					i++;
				} else {
					if (nc == 0 || c[nc - 1] != b[j])
						c[nc++] = b[j];
					j++;
				}
			} else {
				if (i < na) {
					if (nc == 0 || c[nc - 1] != a[i])
						c[nc++] = a[i];
					i++;
				} else {
					if (nc ==0 || c[nc - 1] != b[j])
						c[nc++] = b[j];
					j++;
				}
			}
		}
		return nc;
	}
	
	int[] tin, tout;
	int timer;
	
	void go(int v, int p) {
		pr[0][v] = p;
		tin[v] = timer++;
		for (int i = 1; i < ln; i++) {
			pr[i][v] = pr[i - 1][pr[i - 1][v]];
			for (int j = 0; j < k[i - 1][v]; j++) {
				a[j] = id[j][i - 1][v];
			}
			for (int j = 0; j < k[i - 1][pr[i - 1][v]]; j++) {
				b[j] = id[j][i - 1][pr[i - 1][v]];
			}
			k[i][v] = union(a, b, c, k[i - 1][v], k[i - 1][pr[i - 1][v]]);
			for (int j = 0; j < k[i][v]; j++) {
				id[j][i][v] = c[j];
			}
		}
		for (int to : g[v]) {
			if (to == p)
				continue;
			go(to, v);
		}
		tout[v] = timer++;
	}
	
	boolean isAncestor(int v, int u) {
		return tin[v] <= tin[u] && tout[u] <= tout[v];
	}
	
	int getAncestor(int v, int u) {
		if (isAncestor(v, u))
			return v;
		if (isAncestor(u, v))
			return u;
		for (int i = ln - 1; i >= 0; --i) {
			if (!isAncestor(pr[i][v], u))
				v = pr[i][v];
		}
		return pr[0][v];
	}
	
	int[] res1, res2, res;
	int n1, n2, ans;
	
	void getWay1(int v, int u) {
		if (v == u) {
			for (int i = 0; i < k[0][v]; i++) {
				res1[n1++] = id[i][0][v];
			}
			return;
		}
		for (int i = ln - 1; i >= 0; --i) {
			if (!isAncestor(pr[i][v], u)) {
				for (int j = 0; j < k[i][v]; j++) {
					a[j] = id[j][i][v];
				}
				for (int j = 0; j < n1; j++) {
					b[j] = res1[j];
				}
				n1 = union(a, b, res1, k[i][v], n1);
				v = pr[i][v];
			}
		}
		for (int j = 0; j < k[1][v]; j++) {
			a[j] = id[j][1][v];
		}
		for (int j = 0; j < n1; j++) {
			b[j] = res1[j];
		}
		n1 = union(a, b, res1, k[1][v], n1);
	}
	
	void getWay2(int v, int u) {
		for (int i = ln - 1; i >= 0; --i) {
			if (!isAncestor(pr[i][v], u)) {
				for (int j = 0; j < k[i][v]; j++) {
					a[j] = id[j][i][v];
				}
				for (int j = 0; j < n2; j++) {
					b[j] = res2[j];
				}
				n2 = union(a, b, res2, k[i][v], n2);
				v = pr[i][v];
			}
		}
		for (int j = 0; j < k[0][v]; j++) {
			a[j] = id[j][0][v];
		}
		for (int j = 0; j < n1; j++) {
			b[j] = res1[j];
		}
		n1 = union(a, b, res1, k[0][v], n1);
	}
	
    void solve() throws Exception {
    	int n = sc.nextInt();
    	int m = sc.nextInt();
    	int q = sc.nextInt();
    	g = new ArrayList[n];
    	ln = 0;
    	a = new int[K];
    	b = new int[K];
    	c = new int[K];
    	res1 = new int[K];
    	res2 = new int[K];
    	while ((1 << ln) <= n) ln++;
    	for (int i = 0; i < n; i++) {
    		g[i] = new ArrayList<Integer>();
    	}
    	for (int i = 1; i < n; i++) {
    		int v = sc.nextInt() - 1;
    		int u = sc.nextInt() - 1;
    		g[v].add(u);
    		g[u].add(v);
    	}
    	id = new int[K][ln][n];
    	pr = new int[ln][n];
    	k = new int[ln][n];
    	for (int i = 0; i < m; i++) {
    		int v = sc.nextInt() - 1;
    		if (k[0][v] < K) {
    			id[k[0][v]++][0][v] = i;
    		}
    	}
    	tin = new int[n];
    	tout = new int[n];
    	go(0, 0);
    	res = new int[K];
    	int nn = 0;
    	while (q-- > 0) {
    		int v = sc.nextInt() - 1;
    		int u = sc.nextInt() - 1;
    		int a = getAncestor(v, u);
    		if (u == a) {
    			int tmp = v;
    			v = u;
    			u = tmp;
    		}
    		n1 = n2 = 0;
    		getWay1(v, a);
    		getWay2(u, a);
    		nn = union(res1, res2, res, n1, n2);
    		nn = min(nn, sc.nextInt());
    		out.print(nn);
    		for (int i = 0; i < nn; i++) {
    			out.print(" " + (res[i] + 1));
    		}
    		out.println();
    	}
    }
    
    BufferedReader in;
    PrintWriter out;
    FastScanner sc;
    
    final String INPUT_FILE = "stdin";
    final String OUTPUT_FILE = "stdout";
    
    static Throwable throwable;
    
    public static void main(String[] args) throws Throwable {
        Thread thread = new Thread(null, new Solution(), "", (1 << 26));
        thread.start();
        thread.join();
        thread.run();
        if (throwable != null)
            throw throwable;
    }
    
    
    public void run() {
        try {
            if (INPUT_FILE.equals("stdin"))
                in = new BufferedReader(new InputStreamReader(System.in));
            else
                in = new BufferedReader(new FileReader(INPUT_FILE));
            if (OUTPUT_FILE.equals("stdout"))
                out = new PrintWriter(System.out);
            else
                out = new PrintWriter(new FileWriter(OUTPUT_FILE));
            sc = new FastScanner(in);
            solve();
        } catch (Exception e) {
            throwable = e;
        } finally {
            out.close();
        }
    }
}

class FastScanner {
    BufferedReader reader;
    StringTokenizer strTok;
    
    FastScanner(BufferedReader reader) {
        this.reader = reader;
    }
    
    public String nextToken() throws Exception {
        while (strTok == null || !strTok.hasMoreTokens())
            strTok = new StringTokenizer(reader.readLine());
        return strTok.nextToken();
    }
    
    public boolean EOF() throws Exception {
    	if (strTok != null && strTok.hasMoreTokens()) {
    		return false;
    	} else {
    		String line = reader.readLine();
    		if (line == null)
    			return true;
    		strTok = new StringTokenizer(line);
    		return false;
    	}
    }
    
    public int nextInt() throws Exception {
        return Integer.parseInt(nextToken());
    }
    
    public long nextLong() throws Exception {
        return Long.parseLong(nextToken());
    }
    
    public double nextDouble() throws Exception {
        return Double.parseDouble(nextToken());
    }
}